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Dec 3, 2009 - H-bonded to a H2O surface functional group occupying the adjacent surface site (MM1); (b) monodentate mononuclear arsenate H-bonded to a...
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J. Phys. Chem. C 2009, 113, 21679–21686

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Influence of pH on Initial Concentration Effect of Arsenate Adsorption on TiO2 Surfaces: Thermodynamic, DFT, and EXAFS Interpretations Guangzhi He,† Meiyi Zhang,‡ and Gang Pan* State Key Laboratory of EnVironmental Aquatic Chemistry, Research Center for Eco-EnVironmental Sciences, Chinese Academy of Sciences, Beijing 100085, People’s Republic of China ReceiVed: June 27, 2009; ReVised Manuscript ReceiVed: October 30, 2009

Under the same thermodynamic condition where the total mass of arsenate was fixed, when the initial arsenate was added to TiO2 suspension by multiple batches, adsorption isotherms declined as the multi-batch increased, which was termed initial concentration (C0) effect. The extent of C0 effect decreased gradually as pH decreased from 7.0 to 5.5. Extended X-ray absorption fine structure analysis of 1-batch and 3-batch isotherm samples showed that the relative proportion of bidentate binuclear (BB) and monodentate mononuclear (MM) complex was rarely affected by pH change from 5.5 to 7.0, indicating that the dependence of C0 effect on pH was not due to inner-sphere chemiadsorption. The influence of pH on adsorption was simulated by density functional theory through changing the number of H+ in model clusters. Calculation of adsorption energy showed that BB surface complex was the most thermodynamically favorable mode (-244.5 kJ mol-1) at low pH, but MM surface complex was the most thermodynamically favorable mode (-135.6 to 27.5 kJ mol-1) at intermediate and high pH, which indicated the influence of surface functional groups (-H2O and -OH) on adsorption reaction pathways. As pH decreased, C0 effect weakened gradually because outer-sphere H-bond adsorption became thermodynamically favorable (-203.1 kJ/mol). The dependence of C0 effect on pH showed that traditional equilibrium adsorption constants could not accurately describe the real adsorption equilibrium at solid-liquid interface, because real equilibrium adsorption state is generally a mixture of various outersphere and inner-sphere metastable-equilibrium states. 1. Introduction Oxyanions adsorption on metal-(hydr)oxides are significantly affected by pH, hydration state, and mineral surface charge.1 pH is one of the most crucial parameters governing the adsorption-desorption of metal ions between mineral surface and aqueous solution.2 The surface protonation-deprotonation process controlled by pH modifies the charge density and redox properties of mineral surface, and changes its reactivity and adsorption capacity.1,2 Studies of sulfate at Al- and Fe-(hydr)oxide-H2O interface showed that the thermodynamic favorability of surface complexation was directly related to surface pH condition (surface proton density).1,3 The dependence of oxyanions adsorption on pH created a complicated network of potential reaction pathways. However, the species (i.e., protonated or deprotonated states) of oxyanions in adsorption process at solid-liquid interface is still controversial.4,5 Little is known on the interaction between inner-sphere and outer-sphere complexes and the influence of adjacent surface functional group (-H2O or -OH) on adsorption reaction pathways. So far, the most commonly reported adsorption geometry of oxyanions on metal-(hydr)oxide surfaces was bidentate binuclear (BB) surface complex.1,3–8 However, two crucial issues are neglected. First, the influence of adjacent surface functional group (-H2O and -OH) on adsorption reaction pathways and the stability of surface complex were not considered. Second, most geometric results were obtained from extended X-ray * To whom correspondence should be addressed. Phone: +86-1062849686. Fax: +86-10-62923541. E-mail: [email protected]. † Author e-mail address: [email protected]. ‡ Author e-mail address: [email protected].

absorption fine structure (EXAFS) spectra, but EXAFS spectra cannot accurately measure the structure of outer-sphere complexes because it does not give the information of long-range structure.9 In a related study, a clear initial concentration effect (i.e., C0 effect) was observed in arsenate-TiO2 adsorption system under pH 7.0, where under the same thermodynamic condition, when a series of fixed total mass of arsenate was added by multibatch, adsorption isotherms, and real equilibrium adsorption constants declined as the number of multi-batch increased.10 This new thermodynamic phenomenon could not be interpreted by traditional thermodynamic adsorption theories but was successfully explained by metastable equilibrium adsorption (MEA) theory.10,11 The existence of C0 effect implied that real equilibrium constants, when defined by macroscopic parameters of concentration and adsorption density, was affected by not only thermodynamic condition but also adsorption kinetics. Experimentally measured equilibrium adsorption constants therefore bear the property of inconstancy in nature.10,12 However, C0 effect under different pH conditions has not been studied. The influence of pH on adsorption reaction and C0 effect needs to be further elucidated. Here, the dominant inner-sphere adsorption complexes of arsenate on TiO2 surfaces in multi-batch isotherm samples under pH from 5.5 to 7.0 were analyzed by EXAFS spectroscopy. Density functional theory simulation was used to explore how the adsorption reaction pathways were affected by surface functional groups (-H2O and -OH) and pH. According to calculated adsorption energies, we were able to obtain the thermodynamic favorability sequence of inner-sphere and outer-

10.1021/jp906019e  2009 American Chemical Society Published on Web 12/03/2009

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sphere adsorption reaction pathways under a certain pH range and explain the change of C0 effect under different pH conditions. 2. Theoretical and Experimental Methods 2.1. Theoretical Section. 2.1.1. DFT Calculation. Low-spin and restricted closed-shell DFT-B3LYP calculation formula13,14 and fully optimized calculation strategy were employed to study the adsorption behavior of arsenate on various protonated Ti-(hydr)oxide surfaces. To eliminate boundary effect and reduce charge of the clusters, the hanging bonds of O atoms were saturated with H atoms.5,15,16 Geometries were predicted using 6-31+G(d) basis set for O, H, 6-311+G(d) basis set for As, and LANL2DZ relativistic effective core potential (RECP) basis set for Ti atoms.14,15 It was reported that the surface of anatase TiO2 particle predominantly consisted of (101), (100), and (001) crystal plane,17,18 and the exposition of crystal plane depended on the synthetic technique.19,20 Because of the high computational cost of electronic structure methods,5,15,21 a Ti2O8 cluster of (100) surface was used for DFT calculation. This fragment was reasonably large to describe the typical adsorption sites for arsenate on Ti-(hydr)oxides.1,3,5,21,22 The good agreement of calculated As-O and As-Ti distances with experimental EXAFS results implied that (100) surface was dominant in the TiO2 powder used in this adsorption experiment.10,14 There were two different oxygen atoms O(2) and O(3) in anatase TiO2, which were bonded by two and three titanium atoms, respectively.20 The 8 boundary oxygen in Ti2O8 model cluster were saturated with 12 H atoms to ensure the bonding numbers of O(2) and O(3) were the same as that of anatase bulk structure. This method avoided the over-relaxation of model clusters.5,14,15 Therefore, a [Ti2(OH)4(H2O)4]4+ cluster of TiO2 was used to simulate pH effect and determine the geometry of Ti-AsO4 surface complexes. In addition, we also investigated cluster size effects by using a larger [Ti4O2(OH)8(H2O)6]4+ cluster model of TiO2 (Figure S4 in Supporting Information). The result indicated that the smaller cluster models used here are reliable for studying the adsorption of arsenate on TiO2 surfaces (discussed in Supporting Information). It was reported that an accurate single point energy calculation using a large basis set on the geometry calculated using a small basis set gave results comparable to performing all calculations using a larger basis set.15 Therefore, to improve the estimation of adsorption reaction energies, single point energy calculations were subsequently performed on each optimized gas-phase geometry using 6-311++G (2df, p) basis set for O, H, As, LANL2DZ relativistic effective core potential (RECP) basis set for Ti atoms in combination with the integral equation formalism polarized continuum model (IEFPCM). IEFPCM calculation has been applied to simulate the effect of water molecules on outer coordination sphere (i.e., long-range solvent effect) and estimate the total free energy in solution (including nonelectrostatic terms) for each optimized species.1,13 The single point energies in solution were estimated by UFF (Universal Force Field) atom radii. The DFT calculation was performed using Gaussian03.13 2.1.2. Adsorption Energy and Equilibrium Constant Calculation. The adsorption reaction Gibbs free energy ∆Gads1,20 of arsenate on TiO2 surfaces was calculated as ∆Gads ) Gtot(TiAsO4) - [Gtot(arsenate) + Gtot(TiO2)] (1), where Gtot(Ti-AsO4) is the total Gibbs free energy of Ti-AsO4 adsorption complex, Gtot(arsenate) and Gtot(TiO2) are the total Gibbs free energy of arsenate molecule and TiO2 cluster, respectively. The theoretical equilibrium adsorption constant K was calculated by equation

He et al. ∆Gabs ) -RT ln K (2), where R is the universal gas constant (8.314 × 10-3 kJ/mol · K) and T is Kelvin temperature. 2.2. Experimental Section. 2.2.1. Materials and Chemicals. All solutions were prepared in ultrapure water (resistivity 18 MΩ) obtained with a Liyuan UPW-10N ultrapure water system. Arsenate stock solution was prepared from sodium arsenate (Na2HAsO4 · 7H2O, ACS, 98.0-102.0%, Alfa Aesar China) and stored at 4 °C. Anatase TiO2 (Beijing chemical regents company, China) was used as the adsorbent. BET surface area analysis indicated a surface area of 201.3 m2/g (ASAP-2010, Micromeritics). The particle size distribution, measured with a Mastersizer 2000 analyzer (Malvern, UK), ranged from 0.3 to 2.5 µm. The average particle size was 0.95 µm. 2.2.2. Multibatch Isotherm Experiments under Different pH. Adsorption isotherms of As(V) on anatase TiO2 were conducted in a series of polypropylene tubes under pH 5.5, 6.2, and 7.0, respectively. Under a series of fixed total mass of arsenate, initial arsenate was added by different modes (i.e., 1-batch and 3-batch) to the suspension of TiO2 (1.0 g/L, 30 mL). Details about experiments can be found in a related study.10 Briefly, in 3-batch isotherm experiment, we divided a series of total arsenate into three equal parts and then added them into TiO2 suspension by 3 times at 0, 4, and 8 h. All adsorption experiments were conducted in 0.01 M NaNO3 solution at 25° C. The pH of the reaction system was constantly monitored and adjusted to the desired value (5.5, 6.2, 7.0) with 0.1 mol/L NaOH or 0.1 mol/L HNO3. The tubes were capped and shaken for 24 h. Kinetic experiments indicated that adsorption reached an apparent equilibrium within 4 h (see Figure 2 in ref 10). After 24 h of equilibration, suspensions of 1-batch and 3-batch adsorption experiments were centrifuged and filtered through 0.25 µm nominal pore-size membrane filters prior to analysis. Arsenate concentration was analyzed by hydride generation atomic fluorescence spectrometry (AFS 610, Ruili Beijing). Adsorption density was calculated from the difference between initial and final concentrations of arsenate. The moist solids of adsorption samples were mounted in a 2 mm thick cell and sealed with adhesive PVC tape for EXAFS measurements. The preparation of materials and the specific operation of 1-batch and 3-batch isotherm experiment were specially introduced in a related study.10 All reagents used in this study were analytical grade and labware was acid-washed. 2.2.3. EXAFS Sample Preparation and Data Collection. To study the influence of pH on C0 effect, six comparable adsorption samples under pH 5.5, 6.2, and 7.0 from 1-batch and 3-batch isotherms of As(V) adsorption on anatase TiO2 were prepared for EXAFS measurement. The six samples were generated from the same initial condition (0.80 mmol/L total arsenate and 1.0 g/L TiO2 particle) but different addition modes of arsenate (1-batch and 3-batch). The samples were sealed between two layers of adhesive PVC tape to prevent moisture loss and stored at 4 °C before EXAFS measurement. EXAFS data were collected on beamline 4W1B at Beijing Synchrotron Radiation Facility (BSRF), China. An energy range of -200-1000 eV from the K-absorption edge of As (11868 eV) was used to collect the spectral data under ambient conditions. Si(111) monochromator double crystals (energy resolution 0.5 eV) were utilized to minimize the high harmonics in the incident beam. The spectra of solid-phase samples were collected in fluorescence mode using a Lytle detector because As(V) concentration was low in adsorption samples, and the standard reference As(V) aqueous solutions (Na2AsO4 · 7H2O) was measured in transmission mode. The

Arsenate Adsorption on TiO2 Surfaces

J. Phys. Chem. C, Vol. 113, No. 52, 2009 21681 surfaces.4,10,26 Noncollinear As-O-O-As multiple scattering (MS) contributions to the EXAFS spectrum were fitted to all spectra by correlating the mean-square disorder of the radial distance (σ2) of the As-O single scattering path to σ2 of the MS As-O-O-As path.27,28 Therefore, the multiple scattering effect from AsO4 tetrahedron was included in EXAFS data fitting. The many body amplitude reduction factor (S02) was fixed to 0.9.29,30 More details on the EXAFS analysis were presented in Supporting Information.

Figure 1. Adsorption isotherms of As(V) on TiO2 in 0.01 mol/L NaNO3 solution at 25 °C under different pH. TiO2 particle concentration is 1 g/L. 1-batch stands for a series of total arsenate being added to TiO2 suspension in one time, and 3-batch stands for the total arsenate being added averagely to TiO2 suspension in 3 times every 4 h. EXAFS samples were marked by ellipse, in which the initial total As(V) concentration is 0.80 mmol/L.

fluorescence signal was filtered by a Ge foil to remove the elastically scattered radiation. An average of three scans was performed to achieve an adequate signal/noise ratio. 2.2.4. EXAFS Data Analysis. EXAFS data were analyzed with the Winxas 3.1 program.23 The spectral data were processed by removing the background absorption, normalization, k-space conversion, Fourier transformation and then extracting the EXAFS structural information using WinXAS 3.1 software package. To remove the background absorption, spectra were background-corrected using a two-polynomial fit. Following the background correction, spectra were normalized. Normalized spectra were then converted to frequency (k) space, weighted by k3, and generating k3χ (k) spectra. k3χ (k) in k-space (Å-1) from 2.0 to 12.0 Å-1 was Fourier transformed (FT) using Bessel window function to produce the radial structure function (RSF) in R-space (Å). The coordination numbers (CN) and interatomic distances (R) were then determined by a fitting procedure between the theoretical and the experimental curves.24 The spectra were fitted with theoretical phase shift and amplitude functions of As-O, As-Ti and multiple scattering As-O-O-As paths calculated by ab initio FEFF 8.2 code25 using the cluster of scorodite (FeAsO4 · 2H2O) with the Fe atom replaced by Ti atom. This method has been widely used in the study of arsenate adsorption on Ti- and Al-(hydr)oxide

3. Results and Discussion 3.1. Adsorption Isotherms under Different pH. Initial concentration effect (i.e., C0 effect) refers to the phenomenon that, under the same thermodynamic condition, adsorption isotherms and real equilibrium adsorption constants are affected by reaction kinetic pathways such as the addition modes of arsenate (i.e., 1-batch or multi-batch). The existence of C0 effect implies that real equilibrium adsorption constant, when defined by macroscopic parameters of concentration and adsorption density, bears the property of inconstancy in nature.10 1-batch and 3-batch adsorption isotherms of arsenate on anatase TiO2 at different pH were presented in Figure 1. The adsorption isotherms were empirically well described with Freundlich equations (R2 > 0.99). As shown in Figure 1, arsenate adsorption density increased as pH decreased from 7.0 to 5.5. 3-batch adsorption isotherm was significantly lower than 1-batch adsorption isotherm at pH 7.0. The gap of 1-batch and 3-batch isotherms reduced at pH 6.2. As pH decreased to 5.5, there was almost no difference between 1-batch and 3-batch isotherms. The C0 effect weakened gradually and even disappeared with the decrease of pH from 7.0 to 5.5 (Figure 1), indicating the existence of notable C0 effect at high pH and the dependence of C0 effect on pH in As (V)TiO2 adsorption system. This result showed that the influence of multi-batch (3-batch) addition mode on adsorption isotherm and equilibrium adsorption constant varied with pH. To study the influence of pH on C0 effect, six comparable adsorption samples were chosen for EXAFS measurement to detect the microstructure of adsorbed arsenate under different pH conditions. These six EXAFS samples were denoted by ellipse on isotherms (Figure 1), which had a same initial As(V) concentration (0.80 mmol/L) but under different reaction addition modes of total arsenate (1-batch and 3-batch). 3.2. MicroscopicStructureofAdsorbedArsenate.3.2.1. EXAFS Analysis of Inner-Sphere Complexes. Fourier transform spectra of As(V) K-edge EXAFS for dissolved and adsorbed

Figure 2. (a) Arsenic RSFs (radial structural functions) for 1-batch and 3-batch adsorption samples at different pH. (b) Arsenic RSFs for As(V) aqueous solutions and correlative adsorption samples at different pH. The small peak after the largest peak is the contribution from As-O-O-As multiple scattering (MS). The peak positions are uncorrected for phase shift.

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He et al.

TABLE 1: Summary of As(V) K-edge EXAFS Results for 1-Batch and 3-Batch Adsorption Samples at pH 5.5, 6.2, and 7.0a As-Ti As-O

BB

MM

sample

CN

R (Å)

σ2

CN1

R1 (Å)

σ2

CN2

R2 (Å)

σ2

Res.

CN1/CN2

1-batch pH 5.5 3-batch pH 5.5 1-batch pH 6.2 3-batch pH 6.2 1-batch pH 7.0 3-batch pH 7.0 As(V)-pH 5.5 As(V)-pH 7.0 calculated values

3.9 4.0 4.0 3.9 4.1 4.1 4.1 4.1 4.0

1.68 1.68 1.68 1.68 1.69 1.68 1.68 1.69 1.70

0.002 0.002 0.002 0.002 0.002 0.002 0.004 0.003

1.9 2.2 1.8 2.1 1.8 2.2

3.17 3.26 3.16 3.19 3.17 3.22

0.008 0.01 0.007 0.008 0.007 0.004

1.1 0.9 1.0 0.8 1.1 1.0

3.60 3.61 3.59 3.59 3.59 3.60

0.01 0.008 0.006 0.01 0.001 0.001

8.6 14.2 11.0 9.0 13.2 10.9 6.7 5.3

1.8 2.4 1.7 2.5 1.6 2.2

2.0

3.25

1.0

3.52

a

The amplitude reduction factor (S02) was fixed to 0.9 in fitting process..4,9

arsenate at pH 5.5-7.0 were given in Figure 2. EXAFS measured structural parameters were presented in Table 1. EXAFS results showed that the first coordination shell of As (V) consisted of four oxygen atoms at distance of 1.69 ( 0.01 Å. The second coordination shell of Ti-AsO4 surface complexes at pH 5.5 to 7.0 contained two titanium subshells at As-Ti distances of 3.20 ( 0.05 and 3.60 ( 0.02 Å (Table1). The small peak after the largest As-O peak in Fourier transform was observed in not only adsorption samples but also arsenate solution sample (Figure 2b), so they were obviously not from Ti backscatter but from As-O-O-As multiple scattering that was a common phenomenon for the structure with low Z (MM (3.13 × 1039) >H-bonded complex (3.91 × 1035) under low pH condition, and in the order of MM (1.54 × 10-5) > BB (8.72 × 10-38) >H-bonded complex (5.01 × 10-45) under high pH condition. Therefore, even under the same thermodynamic conditions, the real equilibrium adsorption constant would vary

J. Phys. Chem. C, Vol. 113, No. 52, 2009 21685 with the change of the proportion of different surface complexes in real equilibrium adsorption. 3.4. Microscopic Explanation for pH Dependence of C0 Effect. EXAFS and XANES analysis indicated that the notable C0 effect at pH 7.0 was caused by the increase of the proportion of BB complex from 1-batch to 3-batch addition mode.10,12,22 However, the relative proportion of BB and MM complexes were little affected by pH change from 5.5 to 7.0. Therefore, the dependence of C0 effect on pH was not due to inner-sphere chemiadsorption. It can be expected that TiOH2+, TiOH, and TiO- surface group are coexistent in the actual infinite TiO2 surfaces. The pH controls the relative proportion between them. We simulated the ∆Gads variation of inner-sphere and outersphere adsorption with pH (Figure 5) using the three kinds of surface (Figure 4), which were achievable in DFT calculation. On the basis of the acid dissociation constants of TiO2 surfaces (pKa1 ) 3.8, pKa2 ) 7.8), the adsorption reaction energy (thermodynamic favorability) of arsenate under low pH conditions (5.5 and 6.2) were expected in the region A in Figure 5. DFT results showed that H-bond adsorption became thermodynamically favorable (-203.1 kJ/mol) as pH decreased. Thus, the TiOH2+ surface group and hence the H-bond adsorption complex would exist under the experimental pH conditions (especially under pH 5.5). H-bond adsorption is essentially an outer-sphere electrostatic attraction (Figure 3d), so it was hardly influenced by the addition mode of arsenate (1-batch and 3-batch). Therefore, as the proportion of outer-sphere adsorption complex increased under low pH condition, the C0 effect would weaken and even disappear (Figure 1). The coexistence and interaction of outer-sphere and innersphere adsorptions caused the extreme complicacy of real adsorption processes at solid-liquid interface, which was not taken into account in traditional thermodynamic adsorption theories. Metastable equilibrium adsorption (MEA) theory pointed out that adsorbate would exist on solid surfaces in different forms11,22 (i.e., MEA states) and recognized the influence of adsorption reaction kinetics on the final MEA states (e.g., MM, BB, and H-bonded complexes in this study) that construct real adsorption equilibrium state.10,12,14 Therefore, traditional thermodynamic adsorption theories need to be further developed by taking metastable equilibrium adsorption into account in order to accurately describe real equilibrium properties of surface adsorption. 4. Conclusion The influence of pH on initial concentration (C0) effect of As(V) on TiO2 surfaces was studied by EXAFS spectra and DFT calculation. EXAFS results indicated that the relative proportion of BB and MM complexes were little affected by pH change from 5.5 to 7.0, and hence the dependence of C0 effect on pH was not due to inner-sphere chemiadsorption. The study of the influence of pH on C0 effect motivated the investigation of outer-sphere adsorption by DFT calculation. DFT results indicated that the adsorption of As(V) on TiO2 surfaces involved not only chemical bond but also H-bond, especially at low pH. On the basis of the DFT results, it was suggested that the coexistence of outer-sphere and inner-sphere adsorption weakened the C0 effect under low pH condition. Acknowledgment. The study was supported by NNSF of China (20777090, 20621703) and the Hundred Talent Program of the Chinese Academy of Science. We thank Beijing Synchrotron Radiation Facility (BSRF, China) for providing the beam time and Tiandou Hu, Ziyu Wu, and Yaning Xie for help in EXAFS analysis.

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Supporting Information Available: Details on EXAFS analysis and the discussion on cluster size effects. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Paul, K. W.; Kubicki, J. D.; Sparks, D. L. EnViron. Sci. Technol. 2006, 40, 7717. (2) Xia, S. W.; Pan, G.; Cai, Z. L.; Wang, Y.; Reimers, J. R. J. Phys. Chem. C 2007, 111, 10427. (3) Paul, K. W.; Borda, M. J.; Kubicki, J. D.; Sparks, D. L. Langmuir 2005, 21, 11071. (4) Pena, M.; Meng, X. G.; Korfiatis, G. P.; Jing, C. Y. EnViron. Sci. Technol. 2006, 40, 1257. (5) Sherman, D. M.; Randall, S. R. Geochim. Cosmochim. Acta 2003, 67, 4223. (6) Fendorf, S.; Eick, M. J.; Grossl, P.; Sparks, D. L. EnViron. Sci. Technol. 1997, 31, 315. (7) Grossl, P. R.; Eick, M.; Sparks, D. L.; Goldberg, S.; Ainsworth, C. C. EnViron. Sci. Technol. 1997, 31, 321. (8) Khare, N.; Martin, J. D.; Hesterberg, D. Geochim. Cosmochim. Acta 2007, 71, 4405. (9) Ankudinov, A. L.; Ravel, B.; Rehr, J. J.; Conradson, S. D. Phys. ReV. B 1998, 58, 7565. (10) Pan, G.; Zhang, M. Y.; He, G. Z. EnViron. Sci. Technol., submitted for publication. (11) Pan, G.; Liss, P. S. J. Colloid Interface Sci. 1998, 201, 71. (12) He, G. Z.; Pan, G.; Zhang, M. Y. J. Phys. Chem. C 2009, 113, 17076. (13) Frisch, M. J.; et al. Gaussian03, rev. C.01wis2; Gaussian, Inc.: Wallingford, CT 2004. (14) He, G. Z.; Pan, G.; Zhang, M. Y. J. Phys. Chem. C, submitted for publication. (15) Hu, Z.; Turner, C. H. J. Am. Chem. Soc. 2007, 129, 3863.

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